Lévy processes and infinitely divisible distributions / Ken-iti Sato

Contient des exercices

Bibliogr. p. 451-478. Index

The first two chapters present basics: examples, connection between Lévy processes and infinitely divisible distributions. Chapter 3 treats the stable processes together with selfsimilar and selfdecomposable distributions. In Chapter 4 one finds the Lévy-Itô decomposition of sample functions of Lévy processes. Chapter 5 is devoted to properties of Lévy processes based on their distributions like moments, supports of the Lévy measures, continuity of the distributions. Subordination and time transformation is the topic of Chapter 6. In Chapter 7 the reader finds results on recurrence and transience of the underlying processes, and Chapter 8 contains the potential theory of Lévy processes, which is a generalization of the classical potential theory of the Laplacian, which is connected with the Brownian motion. Chapter 9 presents the Wiener-Hopf factorization and its consequences to short and long time behaviour of Lévy processes. The last Chapter 10 yields additional properties of infinitely divisible distributions.

Every chapter is finished by a series of ambitious exercises and notes, which include additional material, the solutions are given at the end of the book. The notes hint to further results in the literature and give insight into the history of the topics. More than five hundred references, all mentioned in the text, complete the survey on Lévy processes. (Zentralblatt)